trafo_kartezske_orb

> restart:
with(linalg):
with(LinearAlgebra):
q:=<a*(cos(E)-e), a*sqrt(1-e^2)*sin(E),0>;
qdot:=<-n*a*sin(E)/(1-e*cos(E)), n*a*sqrt(1-e^2)*cos(E)/(1-e*cos(E)),0>;
Rxq:=< <
cos(Omega)*cos(omega)-sin(Omega)*cos(i)*sin(omega),
-cos(Omega)*sin(omega)-sin(Omega)*cos(i)*cos(omega),
sin(Omega)*sin(i)>|
<sin(Omega)*cos(omega)+cos(Omega)*cos(i)*sin(omega),
-sin(Omega)*sin(omega)+cos(Omega)*cos(i)*cos(omega),
-cos(Omega)*sin(i)>|
<sin(i)*sin(omega),
sin(i)*cos(omega),
cos(i)>>;
r:=MatrixVectorMultiply(Rxq, q);
rdot:=MatrixVectorMultiply(Rxq, qdot);
X:=r[1];
Y:=r[2];
Z:=r[3];
VX:=rdot[1];
VY:=rdot[2];
VZ:=rdot[3];

Jzp:=((X*VY-Y*VX)/sqrt((X^2+Y^2)*(VX^2+VY^2)));

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n:=sqrt(GM)*a^(-3/2);
omega:=0;
Omega:=0;
#e:=0.15;
#a:=1;
# i:=0;
GM:=1;
#FCE:=(X,Y,Z)->subs(E=X, i=Y/180.0*Pi, e=Z, Jzp);
FCE:=(X,Y,Z,fn)->subs(E=X, i=Y/180.0*Pi, e=Z, a=fn, Jzp);

plot([FCE(x,0,0,1), FCE(x,30,0,1), FCE(x,60,0,1), FCE(x,90,0,1)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed, legend=["(x,0,0,1)", "(x,30,0,1)", "(x,60,0,1)", "(x,90,0,1)"]);

plot([FCE(x,0,0.15,1), FCE(x,30,0.15,1), FCE(x,60,0.15,1), FCE(x,90,0.15,1)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed, legend=["(x,0,0.15,1)", "(x,30,0.15,1)", "(x,60,0.15,1)", "(x,90,0.15,1)"]);

plot([FCE(x,0,0.35,1), FCE(x,30,0.35,1), FCE(x,60,0.35,1), FCE(x,90,0.35,1)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed, legend=["(x,0,0.35,1)", "(x,30,0.35,1)", "(x,60,0.35,1)", "(x,90,0.35,1)"]);

plot([FCE(x,0,0.65,1), FCE(x,30,0.65,1), FCE(x,60,0.65,1), FCE(x,90,0.65,1)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed, legend=["(x,0,0.65,1)", "(x,30,0.65,1)", "(x,60,0.65,1)", "(x,90,0.65,1)"]);

plot([FCE(x,0,0.95,1), FCE(x,30,0.95,1), FCE(x,60,0.95,1), FCE(x,90,0.95,1)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed, legend=["(x,0,0.95,1)", "(x,30,0.95,1)", "(x,60,0.95,1)", "(x,90,0.95,1)"]);
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plot([FCE(x,0,0,1), FCE(x,30,0,1), FCE(x,60,0,1), FCE(x,90,0,1),
FCE(x,0,0,3), FCE(x,30,0,3), FCE(x,60,0,3), FCE(x,90,0,3)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed, legend=["(x,0,0,1)", "(x,30,0,1)", "(x,60,0,1)", "(x,90,0,1)","(x,0,0,3)", "(x,30,0,3)", "(x,60,0,3)", "(x,90,0,3)"]);
plot([FCE(x,0,0,1), FCE(x,30,0,1), FCE(x,60,0,1), FCE(x,90,0,1),
FCE(x,0,0,3), FCE(x,30,0,3), FCE(x,60,0,3), FCE(x,90,0,3)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed);

plot([FCE(x,0,0.15,1), FCE(x,30,0.15,1), FCE(x,60,0.15,1), FCE(x,90,0.15,1),
FCE(x,0,0.15,3), FCE(x,30,0.15,3), FCE(x,60,0.15,3), FCE(x,90,0.15,3)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed, legend=["(x,0,0.15,1)", "(x,30,0.15,1)", "(x,60,0.15,1)", "(x,90,0.15,1)","(x,0,0.15,3)", "(x,30,0.15,3)", "(x,60,0.15,3)", "(x,90,0.15,3)"]);
plot([FCE(x,0,0.15,1), FCE(x,30,0.15,1), FCE(x,60,0.15,1), FCE(x,90,0.15,1),
FCE(x,0,0.15,3), FCE(x,30,0.15,3), FCE(x,60,0.15,3), FCE(x,90,0.15,3)], x=0..2*Pi, y=-1.1..+1.1, axes=boxed);

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E:=Pi;
Omega:=0;
n:=sqrt(GM)*a^(-3/2);
#Jzp_zjednoduseny:=simplify((X*VY-Y*VX)/sqrt((X^2+Y^2)*(VX^2+VY^2)));

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